Ériu is generally believed to have been the matron goddess of Ireland, a goddess of sovereignty, or simply a goddess of the land. The origin of Ériu has been traced to the Proto-Celtic (800 B.C.) reconstruction.
Hibernia (ancient name and Latin variant): apparently assimilated to Latin hibernus ("wintry").
Ireland is known as Eirinn in Scottish Gaelic, from a grammatical case of Éire. In the fellow Celtic languages: in Welsh it is Iwerddon; in Cornish it is Ywerdhon or Worthen; and in Breton it is Iwerzhon.
In Gaelic bardic tradition Ireland is also known by the poetical names of Banbha (meaning "piglet") and Fódhla. The Proto-Indo-European reconstruction of the Irish language suggests a meaning of "abundant land".
It is highly likely that explorers borrowed and modified this term. During his exploration of northwest Europe (circa 320 B.C.), Pytheas of Massilia (350 B.C. - 285 B.C.) called the island Ierne. In his book Geographia (circa A.D. 150), Claudius Ptolemaeus (A.D. 90 - A.D. 168) called the island Iouernia. Based on these historical accounts, the Roman Empire called the island Hibernia.
While Éire is simply the name for the island of Ireland in the Irish language, and sometimes used in English, Erin is a common poetic name for Ireland, as in "Erin go bragh." The distinction between the two is one of the difference between cases of nouns in Irish.